CRITICAL-POINTS OF THE GINZBURG-LANDAU SY STEM ON A RIEMANNIAN SURFACE

We study here the Ginzburg-Landau functional on a Riemannian surface S , endowed with an arbitrary metric E(epsilon) (u) = 1/2 integral(S) \\ del u\\(2) 1/4 epsilon(2) integral(S) (\u\(2) - 1)(2), u is an element of H-1 (S,C), where epsilon is an element of\0, infinity\. We study t he asymptotic behaviour of the critical points for E(epsilon) as epsil on --> 0. We define a renormalized energy which allow to characterize the position of the singularities at the limit.